In this paper
we investigate differences between the Euclidean geometry and the spacetime
geometry. We derive formulas for the proper radius and proper volume of a homogeneous
mass ball. We shall see that the homogeneous ball, whose mass and
radius is the same as that of the Sun, has its circumference about 3 km shorter
than 2Pi r, where r is its proper radius. Similarly, the Earth has its proper volume
about 457 km3 larger than the massless ball with the same circumference.
The difference between the classical Euclidean geometry and the geometry of
a curved spacetime will be most visible for balls corresponding to compact astrophysical
objects such as, e.g., neutron stars.